Find the point on the curve y = x2+3x+4 at which the tangent passes th

1.	Find the point on the curve y = x2+3x+4 at which the tangent passes through the origin.
Answer» If tangent is pass through origin it means that equation of tangent is y = mx Let us suppose that tangent is made at point (x₁, y₁) y₁ = x₁² + 3x₁ + 4 …(1) m : dy/dx = 2x+3 m at (x₁, y₁) = 2x₁ + 3 Equation of tangent : y₁ = (2x₁ + 3)x₁ …(2) On comparing eq(1) and eq(2) x₁² + 3x₁ + 4 = (2x₁ + 3)x₁ x₁² – 4 = 0 ⇒ x₁ = 2 and -2 At x₁ = 2, y₁ = 14 At x₁ = -2, y₁ = 2 So, required points are (2, 14) and (-2, 2)

Find the point on the curve y = x2+3x+4 at which the tangent passes through the origin.

Answer»

If tangent is pass through origin it means that equation of tangent is y = mx

Let us suppose that tangent is made at point (x₁, y₁)

y₁ = x₁² + 3x₁ + 4 …(1)

m : dy/dx = 2x+3

m at (x₁, y₁) = 2x₁ + 3

Equation of tangent : y₁ = (2x₁ + 3)x₁ …(2)

On comparing eq(1) and eq(2)

x₁² + 3x₁ + 4 = (2x₁ + 3)x₁

x₁² – 4 = 0

⇒ x₁ = 2 and -2

At x₁ = 2, y₁ = 14

At x₁ = -2, y₁ = 2

So, required points are (2, 14) and (-2, 2)